{"paper":{"title":"Inverse problems and sharp eigenvalue asymptotics for Euler-Bernoulli operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Andrey Badanin, Evgeny Korotyaev","submitted_at":"2013-09-13T13:38:01Z","abstract_excerpt":"We consider Euler-Bernoulli operators with real coefficients on the unit interval. We prove the following results:\n  i) Ambarzumyan type theorem about the inverse problems for the Euler-Bernoulli operator.\n  ii) The sharp asymptotics of eigenvalues for the Euler-Bernoulli operator when its coefficients converge to the constant function.\n  iii) The sharp eigenvalue asymptotics both for the Euler-Bernoulli operator and fourth order operators (with complex coefficients) on the unit interval at high energy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3449","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}